Transcription of An Example of Two Phase Simplex Method - McMaster …
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An Example of Two Phase Simplex Method - McMaster …
An Example of Two Phase Simplex Method AdvOL @ McMaster , February 2, 2009. Consider the following LP problem. max z = 2x1 + 3x2 + x3. x1 + x2 + x3 40. 2x1 + x2 x3 10. x2 + x3 10. x1 , x 2 , x 3 0. It can be transformed into the standard form by introducing 3 slack variables x4 , x5 and x6 . max z = 2x1 + 3x2 + x3. x1 + x2 + x3 + x4 = 40. 2x1 + x2 x3 x5 = 10. x2 + x3 x6 = 10. x1 , x 2 , x 3 , x 4 , x 5 , x 6 0. There is no obvious initial basic feasible solution, and it is not even known whether there exists one. We can use Phase I Method to find out. Consider the following LP problem derived from the original one by relaxing the second and third constraints and introducing a new objective function. min x7 + x8 , (or max w = x7 x8 ). x1 + x2 + x3 + x4 = 40. 2x1 + x2 x3 x5 + x7 = 10. x2 + x3 x6 + x8 = 10. x1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 , x 8 0. This problem ( Phase I) has an initial basic feasible solution with basic variables being x4 , x7.
The entering and leaving variables would be x1 and x7 respectively: w x1 x2 x3 x4 x5 x6 x7 x8 1 0 1 -1 0 0 1 1 0 = -10 0 0 0.5 1.5 1 0.5 0 -0.5 0 = 35 0 1 0.5 -0.5 0 ...
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